Finite Group Databasebeta

← C22×#63573 #11858385

Subgroups — C22×#63573 #11858385

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic
3C23×C3×C3⋊C8C211yesmaximal, characteristic
4C2×#63573C2112yesmaximal, direct product factor
5C22×#817—31nomaximal
6C22×#808—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C23×C3×Dic3—21no—
10C2×C4⋊(C3⋊Dic3)—23no—
11C2×C4⋊(C3⋊Dic3)C2216yes—
12C2×C3×C4⋊Dic3—23no—
13C2×C3×C4⋊Dic3C2216yes—
14C22×C3×C3⋊C8C418yescomplemented
15C22×C3×C3⋊C8C2216yes—
16#63573C22116yesdirect product factor
17C23×C3×C8—31no—
18C22×C3×C4⋊C4—31no—
19C22×C4⋊Dic3—31no—
20C22×C4⋊Dic3—31no—
21C22×C4⋊Dic3—61no—
22C22×C4⋊Dic3D311yescharacteristic
23C23×C3⋊C8D311yescharacteristic
24C2×#817—312no—
25C2×#808—312no—
26C24×C32D411yescharacteristic
27C22×C32×C4C2×C414yes—
28C22×C32×C4D413yes—
29C22×C32×C4Q814yes—
30C22×C32×C4C2313yes—
31C22×C3⋊Dic3—26no—
32C22×C3⋊Dic3—44no—
33C22×C3×Dic3—26no—
34C22×C3×Dic3—44no—
35C4⋊(C3⋊Dic3)—26no—
36C4⋊(C3⋊Dic3)C2314yes—
37C3×C4⋊Dic3—26no—
38C3×C4⋊Dic3C2314yes—
39C2×C3×C3⋊C8C2×C4124yescomplemented
40C2×C3×C3⋊C8C2314yes—
41C22×#106—91noSylow
42C23×C3×C4—21no—
43C23×C3×C4—61no—
44C23×C3×C4C2×D311yescharacteristic
45C23×C3×C4C2×D311yescharacteristic
46C23×Dic3—21no—
47C23×Dic3—62no—
48C23×Dic3—61no—
49C23×Dic3—61no—
50C22×C3×C8—38no—
51C22×C3×C8—36no—
52C2×C3×C4⋊C4—36no—
53C2×C3×C4⋊C4—63no—
54C2×C4⋊Dic3—23no—
55C2×C4⋊Dic3—36no—
56C2×C4⋊Dic3—36no—
57C2×C4⋊Dic3—66no—
58C2×C4⋊Dic3—66no—
59C2×C4⋊Dic3—63no—
60C2×C4⋊Dic3—63no—
61C2×C4⋊Dic3C2×D316yes—
62C22×C3⋊C8Dic318yescomplemented
63C22×C3⋊C8C2×D316yes—
64#817—316no—
65#808—316no—
66C23×C32C4⋊C414yes—
67C23×C32SD1614yes—
68C23×C32SD1614yes—
69C23×C32C2×D413yes—
70C2×C32×C4C4⋊C4112yes—
71C2×C32×C4C22×C416yes—
72C2×C32×C4C2×D413yes—
73C2×C32×C4C2×Q816yes—
74C2×C32×C4C2411yescharacteristic
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3—412no—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—412no—
79C3×C3⋊C8C22×C418yescomplemented
80C23×C8—31no—
81C22×C4⋊C4—31no—
82C22×C4⋊C4—91no—
83C2×#106—912no—
84C24×C3—21no—
85C24×C3D1211yescharacteristic
86C24×C3#6711yescharacteristic
87C22×C3×C4—24no—
88C22×C3×C4—23no—
89C22×C3×C4—24no—
90C22×C3×C4—23no—
91C22×C3×C4—66no—
92C22×C3×C4—124no—
93C22×C3×C4Dic614yes—
94C22×C3×C4Dic614yes—
95C22×C3×C4C4×D314yes—
96C22×C3×C4D1213yes—
97C22×C3×C4C2×Dic314yes—
98C22×C3×C4#6713yes—
99C22×C3×C4C22×D313yes—
100C22×C3×C4C22×D313yes—
101C22×Dic3—26no—
102C22×Dic3—44no—
103C22×Dic3—612no—
104C22×Dic3—66no—
105C22×Dic3—66no—
106C22×Dic3—128no—
107C22×Dic3—124no—
108C22×Dic3—124no—
109C2×C3×C8—324no—
110C2×C3×C8—34no—
111C3×C4⋊C4—34no—
112C3×C4⋊C4—66no—
113C4⋊Dic3—26no—
114C4⋊Dic3—34no—
115C4⋊Dic3—34no—
116C4⋊Dic3—64no—
117C4⋊Dic3—612no—
118C4⋊Dic3—66no—
119C4⋊Dic3—66no—
120C4⋊Dic3C22×D314yes—
121C2×C3⋊C8C2×Dic3124yescomplemented
122C2×C3⋊C8C22×D314yes—
123C22×C32#106116yescomplemented
124C22×C32C2×C4⋊C416yes—
125C22×C32C2×SD1616yes—
126C22×C32C2×SD1616yes—
127C22×C32C22×D411yescharacteristic
128C32×C4C2×C4⋊C416yes—
129C32×C4C23×C411yescharacteristic
130C32×C4C22×Q811yescharacteristic
131C3⋊Dic3—44no—
132C3×Dic3—44no—
133C23×C4—61no—
134C23×C4—181no—
135C23×C4D3211yescharacteristic
136C22×C8—38no—
137C22×C8—36no—
138C2×C4⋊C4—36no—
139C2×C4⋊C4—63no—
140C2×C4⋊C4—96no—
141C2×C4⋊C4—183no—
142#106—916no—
143C23×C3—24no—
144C23×C3—24no—
145C23×C3—24no—
146C23×C3—23no—
147C23×C3#20414yes—
148C23×C3#20414yes—
149C23×C3Dic3⋊C414yes—
150C23×C3C4⋊Dic314yes—
151C23×C3#21414yes—
152C23×C3#21514yes—
153C23×C3C2×D1213yes—
154C23×C3C2×#6713yes—
155C2×C3×C4—21no—
156C2×C3×C4—212no—
157C2×C3×C4—26no—
158C2×C3×C4—23no—
159C2×C3×C4—26no—
160C2×C3×C4—64no—
161C2×C3×C4—1212no—
162C2×C3×C4Dic3⋊C4112yes—
163C2×C3×C4C4⋊Dic3112yes—
164C2×C3×C4C2×Dic616yes—
165C2×C3×C4C2×Dic616yes—
166C2×C3×C4C2×C4×D316yes—
167C2×C3×C4C2×D1213yes—
168C2×C3×C4C22×Dic316yes—
169C2×C3×C4C2×#6713yes—
170C2×C3×C4C23×D311yescharacteristic
171C2×C3×C4C23×D311yescharacteristic
172C2×Dic3—24no—
173C2×Dic3—412no—
174C2×Dic3—68no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—1224no—
178C2×Dic3—1212no—
179C2×Dic3—1212no—
180C3×C8—38no—
181C3⋊C8C22×Dic318yescomplemented
182C2×C32C2×#106112yescomplemented
183C2×C32C22×C4⋊C411yescharacteristic
184C2×C32C22×SD1611yescharacteristic
185C2×C32C22×SD1611yescharacteristic
186C24#62611yescharacteristic
187C22×C4—66no—
188C22×C4—124no—
189C22×C4—186no—
190C22×C4—364no—
191C22×C4D3×Dic314yes—
192C22×C4#62613yes—
193C22×C4#62714yes—
194C22×C4C2×D3213yes—
195C2×C8—34no—
196C2×C8—324no—
197C4⋊C4—34no—
198C4⋊C4—66no—
199C4⋊C4—94no—
200C4⋊C4—186no—
201C22×C3—21no—
202C22×C3—26no—
203C22×C3—216no—
204C22×C3—26no—
205C22×C3—26no—
206C22×C3#808116yescomplemented
207C22×C3#817116yescomplemented
208C22×C3C2×#20416yes—
209C22×C3C2×#20416yes—
210C22×C3C2×Dic3⋊C416yes—
211C22×C3C2×C4⋊Dic316yes—
212C22×C3C2×#21416yes—
213C22×C3C2×#21516yes—
214C22×C3C22×D1211yescharacteristic
215C22×C3C22×#6711yescharacteristic
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—26no—
219C3×C4—124no—
220C3×C4C2×Dic3⋊C416yes—
221C3×C4C2×C4⋊Dic316yes—
222C3×C4C22×Dic611yescharacteristic
223C3×C4C22×Dic611yescharacteristic
224C3×C4C22×C4×D311yescharacteristic
225C3×C4C23×Dic311yescharacteristic
226Dic3—44no—
227Dic3—128no—
228Dic3—124no—
229Dic3—124no—
230C32C22×#10611yescharacteristic, complemented, Sylow
231C23#371614yes—
232C23#371714yes—
233C23Dic3⋊Dic314yes—
234C23C2×#62613yes—
235C2×C4—64no—
236C2×C4—1212no—
237C2×C4—184no—
238C2×C4—3612no—
239C2×C4Dic3⋊Dic3112yes—
240C2×C4C2×D3×Dic316yes—
241C2×C4C2×#62613yes—
242C2×C4C2×#62716yes—
243C2×C4C22×D3211yescharacteristic
244C8—38no—
245C2×C3—212no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3C2×#808112yescomplemented
250C2×C3C2×#817112yescomplemented
251C2×C3C22×#20411yescharacteristic
252C2×C3C22×#20411yescharacteristic
253C2×C3C22×Dic3⋊C411yescharacteristic
254C2×C3C22×C4⋊Dic311yescharacteristic
255C2×C3C22×#21411yescharacteristic
256C2×C3C22×#21511yescharacteristic
257C22#63573116yesdirect product factor
258C22C2×#371616yes—
259C22C2×#371716yes—
260C22C2×Dic3⋊Dic316yes—
261C22C22×#62611yescharacteristic
262C4—124no—
263C4—364no—
264C4C2×Dic3⋊Dic316yes—
265C4C22×D3×Dic311yescharacteristic
266C4C22×#62711yescharacteristic
267C3—21no—
268C3C22×#80811yescharacteristic, complemented
269C3C22×#81711yescharacteristic, complemented
270C2C2×#63573112yesdirect product factor
271C2C22×#371611yescharacteristic
272C2C22×#371711yescharacteristic
273C2C22×Dic3⋊Dic311yescharacteristic
subgroupG/H
centerC24#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32D4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C22×#106
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#63573C2direct (N × H)
14. C22×C3×C3⋊C8C4semidirect
16. #63573C22direct (N × H)
39. C2×C3×C3⋊C8C2×C4semidirect
62. C22×C3⋊C8Dic3semidirect
79. C3×C3⋊C8C22×C4semidirect
121. C2×C3⋊C8C2×Dic3semidirect
123. C22×C32#106semidirect
181. C3⋊C8C22×Dic3semidirect
182. C2×C32C2×#106semidirect
206. C22×C3#808semidirect
207. C22×C3#817semidirect
230. C32C22×#106semidirect
249. C2×C3C2×#808semidirect
250. C2×C3C2×#817semidirect
257. C22#63573direct (N × H)
268. C3C22×#808semidirect
269. C3C22×#817semidirect
270. C2C2×#63573direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×C4⋊Dic32
C23×C3×C3⋊C82
C2×#635732
C22×#8173
C22×#8083